While DP systems are not affected by thermally induced fluctuations in the volume of product in a tank, they can be adversely influenced by thermal changes that act directly upon the components of the measurement system and the piping that interconnects these
components. Referring to Figure 3, one can see that the pressure sensor, standpipe, and interconnecting piping are mounted on the tank exterior; these components therefore experience generally greater temperature changes than those occurring in the product contained in the tank. As a result, careful accounting must be made for the influence these thermal changes have on the sensor output.
Given the configuration shown in Figure 3, the output of the DP system can be described by the following equation:
AP,-APi = pTrh,,- PTi'oi + (h2 + hJ (PT,- P T i ) - h,(p, - P N i ) - h2@, - P P i )
- ( ~ s p f i , - P s p i k i ) - W s p j - P s p i ) - M p p f - P p i ) (2) In this relation, the left hand term represents the output from the differential pressure sensor.
The first term on the right hand side of the equation represents the change of mass occurring in the tank, while all other right hand terms are attributable to corrections required as a result of the physical arrangement of instrumentation piping. Examination of this relationship yields some insights into sources of potential measurement error, and provides a mechanism from which an optimum differential-pressure measurement system can be developed. The equation implies that the DP sensor's output, while directly infiuenced by changes in product mass in the tank, is also influenced by the density changes that occur in the vertical legs of the piping connecting the sensor to both the tank and the standpipe. These influences can be minimized by configuring the sensor and standpipe so that only horizontal piping
connections are employed. Further reductions in unwanted sensor output can be obtained by minimizing the length of these horizontal runs.
Because the current experimental configuration employed some vertical instrumentation runs, additional temperature sensors were placed on selected piping runs in order to permit the sensor output to be compensated for thermal effects. The output from these sensors, along with measured physical dimensions of the interconnecting piping, was incorporated into Eq. (2) to estimate the thermal influence on the output of the DP sensor.
The results of the calculations in Eq. (2) are shown in Figure 10, along with the gross volume changes measured by the DP sensor. According to these data, a considerable fraction of the
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interconnecting piping. Even after these thermal effects have been accounted for, however, the residual volume fluctuations are sufficiently large that they preclude the conduct of a reliable leak test. These residual fluctuations are suggestive of additional thermal effects on the output of the DP sensor.
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Figure 10. Thermally induced level fluctuations attributable to instrumentation piping (lower plot). The gross level measurements (upper plot) are also shown for comparison. Both plots depict the voluine of oil, in thousands of gailons, in a i 17-ft-diameter tank.
The most obvious of these effects is that of thermal sensitivity of the differential pressure sensor. The manufacturer’s performance specifications provide some insights into how much thermal influence can be expected. In the current experiments, fluctuations of approximately 8 galPC could be expected. Additional experiments were conducted to try to confirm these predicted thermally induced volume fluctuations.
The results of these tests, for a sensor span of 1.7 in. H,O, are shown in Figure 1 1. The data in Figure 11 characterize the particular sensor used to obtain thermal measurements of the product contained in the tank; these data suggest that a factor of -6.9 gal/”C should be used i n the analysis of the current experimental data.
Application of the pressure sensor thermal factor to the data shown in Figure 1 1 is helpful in compensating for a portion of the residual level fluctuations. However, even after
incorporating this correction, and then fully compensating for all other quantified sources of level fluctuation (shell growth, thermal lift, and thermal effects on instrumentation piping), a significant diurnal level fluctuation is still present in the data. This residual fluctuation, shown in
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Not for Resale No reproduction or networking permitted without license from IHS
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Figure 11. Change in differential pressure sensor output due to changes in sensor temperature. The plot depicts the volume of oil, in thousands of gallons, in a 117-ft-diameter tank. A constant liquid differential of 1.25 in.
H,O was applied to the sensor.
Figure 12, is sufficiently large to preclude the conduct of a viable leak detection test over a short time period. The data clearly suggest that there are additional diurnal influences that must be identified and compensated for in order to be able to detect small leak rates.
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Figure 12. Residual levei fluctuation after for thermal effects on both the tank and the measurement instrumentation have been fully compensated for. The plot depicts the level of oil, expressed in terms of volume (in thousands of gallons), in a 117-ft-diameter tank.
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The source of these residual diurnal level fluctuations is not clearly understood. While these changes appear to be attributable to thermal influences, a clear physical mechanism which would account for them has not been identified. The strong changes which occur during the morning and evening hours (periods in which the rate of change of temperature is strongest) may be responsible for some of the observed fluctuations, particularly if the measurement system response lags behind the ambient temperature changes. Another possible source of error may be attributed to the effect of vertical piping runs on the measurement system output. In spite of the extensive number of thermal sensors placed on the DP
instrumentation, unaccounted-for thermal influences may still occur, particularly at the point where the high pressure tap enters the tank via a short length of vertical tubing. These potential error sources should be minimized by eliminating as much vertical piping as possible: the ideal installation would be totally devoid of any vertical piping runs.